Cosmological Evolution of the Duty Cycle of Quasars

Quasars are powered by accretion onto supermassive black holes, but theproblem of the duty cycle related to the episodic activity of the black holesremains open as one of the major questions of cosmological evolution ofquasars. In this Letter, we obtain quasar duty cycles based on analyses of alarge sample composed of 10,979 quasars with redshifts $z\le2.1$ from the SloanDigital Sky Survey (SDSS) Data Release Three. We estimate masses of quasarblack holes and obtain their mass function (MF) of the present sample. We thenget the duty cycle $\bar{\delta}(z)=10^{-3}\sim 1$ based on the So{\l}tan'sargument, implying that black holes are undergoing multiple episodic activity.We find that the duty cycle has a strong evolution. By comparison, we show thatevolution of the duty cycle follows the history of cosmic star formation rate(SFR) density in the Universe, providing intriguing evidence for a naturalconnection between star formation and triggering of black hole activity.Feedback on star formation from black hole activity is briefly discussed.Comment: Accepted by ApJL, 4 pages and 2 Figure